Exam 10: Two-Sample Tests

TABLE 10-10 The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different. -Referring to Table 10-10, construct a 90% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

TABLE 10-7 To investigate the efficacy of a diet, a random sample of 16 male patients is drawn from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t-test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds. -Referring to Table 10-7, the t test should be ____-tailed.

TABLE 10-9 A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi. Males: $n = 109 , p _ { M } = 0.422018 \quad$ Females: $n = 52 , p _ { F } = 0.25$ $p M - p F = 0.172018 \quad \quad \quad \quad \quad Z = 211825$ -Referring to Table 10-9, construct a 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

TABLE 10-14 A problem with a telephone line that prevents a customer from receiving or making calls is disconcerting to both the customer and the telephone company. The data on samples of 20 problems reported to two different offices of a telephone company and the time to clear these problems (in minutes) from the customers' lines are collected. Below is the Excel output to see whether there is evidence of a difference in the mean waiting time between the two offices assuming that the population variances in the two offices are not equal. t- Test: Two- Sample Assuming Unequal Variances Office 1 Office 2 Mean 2214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 38 Stat 0.354386 (<=) one- tail 0.362504 Critical one- tail 1.685953 (<=) two- tail 0.725009 Critical two- tail 2.024394 -Referring to Table 10-14, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.10?

TABLE 10-12 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Table 10-12, the p-value of the test is_____ .

TABLE 10-13 A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as "Group 1" and Russell is designated as "Group 2," perform the appropriate test at a level of significance of 0.01. -Referring to Table 10-13, the null hypothesis will be rejected if the test statistic is _____.

The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Assuming W designates women's responses and M designates men's, what hypothesis should The Wall Street Journal test in order to show that its claim is true?

TABLE 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Table 10-5, the number of degrees of freedom is

TABLE 10-14 A problem with a telephone line that prevents a customer from receiving or making calls is disconcerting to both the customer and the telephone company. The data on samples of 20 problems reported to two different offices of a telephone company and the time to clear these problems (in minutes) from the customers' lines are collected. Below is the Excel output to see whether there is evidence of a difference in the mean waiting time between the two offices assuming that the population variances in the two offices are not equal. t- Test: Two- Sample Assuming Unequal Variances Office 1 Office 2 Mean 2214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 38 Stat 0.354386 (<=) one- tail 0.362504 Critical one- tail 1.685953 (<=) two- tail 0.725009 Critical two- tail 2.024394 -Referring to Table 10-14, what assumptions are necessary for testing if there is evidence of a difference in the variability of the waiting time between the two offices to be valid?

TABLE 10-3 The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below. Preservative A Preservative B =106.4 hours =96.54 hours =10.3 hours =13.4 hours -Referring to Table 10-3, suppose ? = 0.05. Which of the following represents the result of the relevant hypothesis test?

TABLE 10-4 A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. $\text { Gotham: } \bar{X} _ { G } = 35 \text { months, } s _G ^ { 2 } = 900 \quad \text { Metropolis: }\bar{X} _ { M } = 50 \text { months, } \mathrm { sm } ^ { 2 } = 1050$ -Referring to Table 10-4, what is the estimated standard error of the difference between the 2 sample means?

TABLE 10-6 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Table 10-6, a two-tailed test of the null hypothesis of no difference would_____(be rejected/not be rejected) at the ? = 0.05 level of significance.

TABLE 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Table 10-5, the calculated value of the test statistic is_____ .

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.

TABLE 10-14 A problem with a telephone line that prevents a customer from receiving or making calls is disconcerting to both the customer and the telephone company. The data on samples of 20 problems reported to two different offices of a telephone company and the time to clear these problems (in minutes) from the customers' lines are collected. Below is the Excel output to see whether there is evidence of a difference in the mean waiting time between the two offices assuming that the population variances in the two offices are not equal. t- Test: Two- Sample Assuming Unequal Variances Office 1 Office 2 Mean 2214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 38 Stat 0.354386 (<=) one- tail 0.362504 Critical one- tail 1.685953 (<=) two- tail 0.725009 Critical two-tail 2.024394 -Referring to Table 10-14, suppose ? = 0.05. Which of the following represents the correct conclusion?

TABLE 10-8 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Primary Secondary 1 \ 55 \ 45 \ 10 2 \ 48 \ 47 \ 1 3 \ 31 \ 32 -\ 1 4 \ 83 \ 77 \ 6 5 \ 37 \ 37 \ 0 6 \ 55 \ 54 \ 1 Sum: \ 309 \ 292 \ 17 Sum of Squares: \ 17,573 \ 15,472 \ 139 -Referring to Table 10-8, the decision rule is to reject the null hypothesis if _______.

TABLE 10-11 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let ×and × represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. -Referring to Table 10-11, what is/are the critical value(s) when testing whether population proportions are different if ? = 0.10?

TABLE 10-3 The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below. Preservative A Preservative B =106.4 hours =96.54 hours =10.3 hours =13.4 hours -Referring to Table 10-3, what assumptions are necessary for testing if the population variances differ for preservatives I and II?

The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. What is the value of the test statistic?

TABLE 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 -Referring to Table 10-5, one must assume that the population of difference scores is normally distributed.